// https://leetcode.cn/problems/sudoku-solver/

// 题干：编写一个程序，通过填充空格来解决数独问题。
//      数独的解法需 遵循如下规则：
//      数字 1-9 在每一行只能出现一次。
//      数字 1-9 在每一列只能出现一次。
//      数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
//      数独部分空格内已填入了数字，空白格用 '.' 表示。

// 示例：输入：board = [["5","3",".",".","7",".",".",".","."],
//      ["6",".",".","1","9","5",".",".","."],
//      [".","9","8",".",".",".",".","6","."],
//      ["8",".",".",".","6",".",".",".","3"],
//      ["4",".",".","8",".","3",".",".","1"],
//      ["7",".",".",".","2",".",".",".","6"],
//      [".","6",".",".",".",".","2","8","."],
//      [".",".",".","4","1","9",".",".","5"],
//      [".",".",".",".","8",".",".","7","9"]]
//输出：[["5","3","4","6","7","8","9","1","2"],
//      ["6","7","2","1","9","5","3","4","8"],
//      ["1","9","8","3","4","2","5","6","7"],
//      ["8","5","9","7","6","1","4","2","3"],
//      ["4","2","6","8","5","3","7","9","1"],
//      ["7","1","3","9","2","4","8","5","6"],
//      ["9","6","1","5","3","7","2","8","4"],
//      ["2","8","7","4","1","9","6","3","5"],
//      ["3","4","5","2","8","6","1","7","9"]]

// 碎语：参照LC36有效的数独，就明白怎么剪枝，本题遍历数组中的每一个数字即可
//       当连续九个数字都填入失败的时候，这个时候已经要放弃这条线，需要一个返回值，因此dfs函数需要返回一个bool结果

#include <bits/stdc++.h>
using namespace std;

class Solution
{
    bool row[9][10];
    bool col[9][10];
    bool grid[3][3][10];
public:
    void solveSudoku(vector<vector<char>>& board)
    {
        // 本质上使用空间换时间,先扫一遍，先把哈希表存一遍
        memset(row, 0, sizeof(row));
        memset(col, 0, sizeof(col));
        memset(grid, 0, sizeof(grid));

        for (int i = 0 ; i < 9 ; i++){ // 行数
            for (int j = 0 ; j < 9 ; j++){ // 列数
                if (board[i][j] == '.') continue;
                else {
                    int digit = board[i][j] - '0';
                    row[i][digit] = true, col[j][digit] = true, grid[i / 3][j / 3][digit] = true;
                }
            }
        }
        dfs(board);

    }

    bool dfs(vector<vector<char>>& board)
    {
        // 先找到没有填过的位置
        int i, j;
        for (i = 0 ; i < 9 ; i++){
            for (j = 0 ; j < 9 ; j++){
                if (board[i][j] == '.'){ // 开始填数
                    for (int num = 1 ; num <= 9 ; num++){
                        if (!row[i][num] && !col[j][num] && !grid[i / 3][j / 3][num]){
                            board[i][j] = '0' + num;
                            row[i][num] = col[j][num] = grid[i / 3][j / 3][num] = true;

                            if (dfs(board)) return true; // 重点理解

                            // 恢复现场
                            board[i][j] = '.';
                            row[i][num] = col[j][num] = grid[i / 3][j / 3][num] = false;
                        }
                    }
                    return false; // 重点理解
                }
            }
        }
        return true; // 重点理解
    }
};

int main()
{
    Solution sol;
    vector<vector<char>> board = {
            {'5','3','.','.','7','.','.','.','.'},
            {'6','.','.','1','9','5','.','.','.'},
            {'.','9','8','.','.','.','.','6','.'},
            {'8','.','.','.','6','.','.','.','3'},
            {'4','.','.','8','.','3','.','.','1'},
            {'7','.','.','.','2','.','.','.','6'},
            {'.','6','.','.','.','.','2','8','.'},
            {'.','.','.','4','1','9','.','.','5'},
            {'.','.','.','.','8','.','.','7','9'}
    };

    sol.solveSudoku(board);
    for (const auto& str : board){
        for (const auto& ch : str){
            cout << ch << " ";
        }
        cout << endl;
    }

    return 0;
}